Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media
The evaluation of direct exchange areas (DEA) in zonal method is the most important task due to the heavy computer cost of multi-integrals together with the existing of singularities. A technique of variable transformation to reduce the fold of integrals, which was developed originally by Erkku (195...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2015-01-01
|
Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2015/703823 |
id |
doaj-ca5220c64e3d4f6588af97811fd5b26a |
---|---|
record_format |
Article |
spelling |
doaj-ca5220c64e3d4f6588af97811fd5b26a2020-11-24T22:44:06ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/703823703823Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering MediaGuo-Jun Li0Ben-Wen Li1Ya-Song Sun2School of Materials & Metallurgy, Northeastern University, Shenyang 110819, ChinaInstitute of Thermal Engineering, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, ChinaBeijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing 102206, ChinaThe evaluation of direct exchange areas (DEA) in zonal method is the most important task due to the heavy computer cost of multi-integrals together with the existing of singularities. A technique of variable transformation to reduce the fold of integrals, which was developed originally by Erkku (1959) to calculate the DEAs of uniformly zonal dividing cylindrical system, was extended by Tian and Chiu (2003) for nonuniformly zonal dividing cylindrical system with large thermal gradients. In this paper, we further extend the reduced integration scheme (RIS) to calculate the DEAs in three-dimensional rectangular system. The detail deductions of six-, five-, and fourfold integrals to threefold ones are presented; the DEAs in a rectangular system with assumption of gray medium are computed by the Gaussian quadrature integration (GQI) and the RIS comparatively. The comparisons reveal that the RIS can provide remarkable higher accuracy and efficiency than GQI. More interestingly and practicably, the singularities of DEAs can be decomposed and weakened obviously by RIS.http://dx.doi.org/10.1155/2015/703823 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Guo-Jun Li Ben-Wen Li Ya-Song Sun |
spellingShingle |
Guo-Jun Li Ben-Wen Li Ya-Song Sun Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media Mathematical Problems in Engineering |
author_facet |
Guo-Jun Li Ben-Wen Li Ya-Song Sun |
author_sort |
Guo-Jun Li |
title |
Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media |
title_short |
Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media |
title_full |
Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media |
title_fullStr |
Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media |
title_full_unstemmed |
Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media |
title_sort |
extension of the reduced integration scheme to calculate the direct exchange areas in 3d rectangular enclosures with nonscattering media |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2015-01-01 |
description |
The evaluation of direct exchange areas (DEA) in zonal method is the most important task due to the heavy computer cost of multi-integrals together with the existing of singularities. A technique of variable transformation to reduce the fold of integrals, which was developed originally by Erkku (1959) to calculate the DEAs of uniformly zonal dividing cylindrical system, was extended by Tian and Chiu (2003) for nonuniformly zonal dividing cylindrical system with large thermal gradients. In this paper, we further extend the reduced integration scheme (RIS) to calculate the DEAs in three-dimensional rectangular system. The detail deductions of six-, five-, and fourfold integrals to threefold ones are presented; the DEAs in a rectangular system with assumption of gray medium are computed by the Gaussian quadrature integration (GQI) and the RIS comparatively. The comparisons reveal that the RIS can provide remarkable higher accuracy and efficiency than GQI. More interestingly and practicably, the singularities of DEAs can be decomposed and weakened obviously by RIS. |
url |
http://dx.doi.org/10.1155/2015/703823 |
work_keys_str_mv |
AT guojunli extensionofthereducedintegrationschemetocalculatethedirectexchangeareasin3drectangularenclosureswithnonscatteringmedia AT benwenli extensionofthereducedintegrationschemetocalculatethedirectexchangeareasin3drectangularenclosureswithnonscatteringmedia AT yasongsun extensionofthereducedintegrationschemetocalculatethedirectexchangeareasin3drectangularenclosureswithnonscatteringmedia |
_version_ |
1725692957766451200 |